JEE 2023 — Mathematics PYQ

1. Tangent ki Equation nikalna:

Diya gaya curve hai $y=x^3$.

Iska slope nikalne ke liye differentiate karte hain:

Point $(-1,-1)$ par slope ($m$):

Ab tangent ki equation ($y-y_1=m(x-x_1)$):

2. Intersection Points dhundhna:

Humein dekhna hai ki tangent curve ko aur kahan kat-ti hai:

Kyuki $(-1,-1)$ point of tangency hai, iska matlab $(x+1{)}^2$ ek factor hoga. Equation ko solve karne par:

Toh intersection points mil gaye: $x=-1$ aur $x=2$.

3. Area Calculate karna:

Humein curve aur line ke beech ka area nikalna hai:

Ab integrate karte hain:

Limits apply karne par:

Sahi Option: (4)